How should I practice Maximum Nesting Depth of Parentheses?

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Maximum Nesting Depth of Parentheses

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Problem statement

Given a string expression whose parentheses are balanced, return the maximum number of simultaneously open parentheses at any position.

Characters other than ( and ) do not affect the depth.

Function

maxDepth(expression: String) → int

Examples

Example 1

expression = "(1+(2*3)+((8)/4))+1"return = 3

The innermost parentheses around 8 are nested inside two other open pairs.

Example 2

expression = "(1)+((2))+(((3)))"return = 3

The final term opens three parenthesis pairs before closing any of them.

Example 3

expression = "1+2"return = 0

The expression contains no parentheses.

Constraints

1 <= expression.length <= 100000
expression contains printable ASCII characters.
The parentheses in expression are balanced.